How can I make multiple mirror websites on the fly?

How can I make multiple mirror websites on the fly, transparently, seemingly created, from multiple donor sites?
For example hxxp://website.that-i-want-to-mirror.net/ to my hxxp://mymirror.website.com on dedicated server with WINDOWS or LINUX?
Without IFRAME, FRAME, etc.
So it looks like my domain, my html code output when “view source” done.
Is there any software proxy that sits in the process and when accessed to my specific domain creates WebPages on the fly from specific domain I pointed at and attaches codes or replaces code to output WebPages, let’s say to the </body> tag or any other tag or string or regexp, etc.
For now I use offline copier like teleport pro, or offline browser but this is time consuming, space, effort, traffic etc and old-school and inefficient.
I make offline copy of a desired website, for example it takes 600 MB space and 235 000 files and many hours of downloading and uploading and tweaking and it’s already outdated. Then upload it to my server and show it through hxxp://mymirror.website.com and then show it. And if I want to make 20 mirrored websites this tasks become impossible to do….
I want it seemingly output through my domain name, may be by CURL, SOCKET, or any other means….
Any ideas and suggestions, guys?